1. Field
Embodiments described herein relate to detecting intersections of a tube-of-response and a reconstruction space in positron emission tomography.
2. Background
The use of positron emission tomography (PET) is growing in the field of medical imaging. In PET imaging, a radiopharmaceutical agent is introduced into an object to be imaged 15, shown in FIG. 1, via injection, inhalation, or ingestion. After administration of the radiopharmaceutical, the physical and bio-molecular properties of the agent will cause the agent to concentrate at specific locations in the human body (i.e., object 15). The actual spatial distribution of the agent, the intensity of the region of accumulation of the agent, and the kinetics of the process from administration to eventually elimination are all factors that may have clinical significance. During this process, a positron emitter attached to the radiopharmaceutical agent will emit positrons according to the physical properties of the isotope, such as half-life, branching ratio, etc.
The radionuclide emits positrons, and when an emitted positron collides with an electron, an annihilation event occurs, wherein the positron and electron are destroyed. Most of the time, an annihilation event produces two gamma rays at 511 keV traveling at substantially 180 degrees apart.
By detecting the two gamma rays, and drawing a line between their locations, i.e., the line-of-response (LOR), one can retrieve the likely location of the original disintegration. While this process will only identify a line of possible interaction, by accumulating a large number of those lines, and through a tomographic reconstruction process, the original distribution can be estimated. In addition to the location of the two scintillation events, if accurate timing (within few hundred picoseconds) is available, a time-of-flight (TOF) calculation can add more information regarding the likely position of the event along the line. Limitations in the timing resolution of the scanner will determine the accuracy of the positioning along this line. Limitations in the determination of the location of the original scintillation events will determine the ultimate spatial resolution of the scanner, while the specific characteristics of the isotope (e.g., energy of the positron) will also contribute (via positron range and co-linearity of the two gamma rays) to the determination of the spatial resolution the specific agent.
The collection of a large number of events creates the necessary information for an image of an object to be estimated through tomographic reconstruction. Two detected events occurring at substantially the same time at corresponding detector elements form a line-of-response that can be histogrammed according to their geometric attributes to define projections, or sinograms, to be reconstructed. Events can also be added to the image individually.
The fundamental element of the data collection and image reconstruction is therefore the LOR, which is the line traversing the system-patient aperture. Additional information can be obtained regarding the location of the event. First, it is known that, through sampling and reconstruction, the ability of the system to reconstruct or position a point is not space-invariant across the field of view, but is better in the center, slowly degrading toward the periphery. A point-spread-function (PSF) is typically used to characterize this behavior. Tools have been developed to incorporate the PSF into the reconstruction process. Second, the time-of-flight, or time differential between the arrival of the gamma ray on each detector involved in the detection of the pair, can be used to determine where along the LOR the event is more likely to have occurred.
The above described detection process must be repeated for a large number of annihilation events. While each imaging case must be analyzed to determine how many counts (i.e., paired events) are required to support the imaging task, current practice dictates that a typical 100-cm long, FDG (fluoro-deoxyglucose) study will need to accumulate several hundred million counts. The time required to accumulate this number of counts is determined by the injected dose of the agent and the sensitivity and counting capacity of the scanner.
While a PET detector can only detect single interactions, i.e., one gamma ray interacting with a crystal and generating light through a scintillation process, PET events are defined by two of those detections occurring at substantially the same time or in coincidence, at substantially 511 keV, and in a geometry compatible with the annihilation event to have occurred in an object of interest 15. It is therefore required for a PET system to properly identify the timeline for each event in order to correctly match or pair events. This is typically accomplished by constructing a complex network of real-time comparators. As the requirement for count rate is also very demanding (up to hundreds of millions of single events per second), the construction of the coincidence circuitry also needs to handle a very large numbers of counts.
Because of the high demand on efficiency, i.e., being able to receive and process hundreds of millions of events per second, the design of the coincidence circuitry is typically one of the most important elements of the PET detection system. Trigger lines are typically brought to centralized hardware for comparison. Usually the coincidence window, or the period of time within which two events will be deemed to be “at the same time,” is set from high-level system controls and does not typically vary during a study or even between studies.
In summary, in PET imaging, a certain kind of radiopharmaceutical with a radioactive isotope (e.g., F-18) is injected into a patient or an object 15. The isotope has an unstable nucleus that undergoes one or several transitions and emits positrons. One positron can annihilate with an electron and produce two 511-keV photons that are emitted in the opposite direction of almost 180 degrees. The aforementioned photons are then captured by a pair of crystals 10 (i.e., scintillation crystals such as LYSO) in a PET ring 20 and recorded by electric circuits, as is illustrated in FIG. 1.
The PET reconstruction process finds the amount and the location of isotopes (unknown) in the patient from the data recorded in the PET system (known). The basic question in the PET reconstruction process is which locations (represented by voxels in the reconstruction space) contribute to a given pair of crystals 10.
To address this question, a certain algorithm is designed to calculate intersections of a line-of-response (LOR) or tube-of-response (TOR, which is a polyhedron formed by connecting corresponding corners of a pair of crystals 10) and a reconstruction space. The aforementioned intersections (i.e., voxels) contributing to a particular pair of crystals 10 (partially or completely) are calculated and updated using a reconstruction algorithm. FIG. 2A shows a three-dimensional (3D) illustration of tube-of response 30 formed by connecting four (4) corners of each crystal 10. FIG. 2B shows intersected voxels 55 of tube-of-response 30 and the reconstruction space 50 (represented by voxels) in a two-dimensional (2D) view.
A conventional formula used in the iterative Ordered Subset Expectation Maximization (OSEM) reconstruction is shown in Equation 1:
            f      _        j          k      +      1        =                              f          _                j        k                    Q        j              ⁢                  ∑                  i          ∈                      Sub            t                                                        ⁢                                    a            ij                    ⁢                      Y            i                                                              ∑                                                j                  ′                                =                1                            m                        ⁢                                          a                if                            ⁢                                                f                  _                                                  j                  ′                                k                                              +                      R            i                    +                      S            i                              
In Equation 1, aij is the probability of voxel j contributing to the TORi, Qi is the normalization term, fj is the activity of voxel j, Yi is the detected photons in TORi, Subt is the tth subset, and Ri and Si are random and scatter counts along TORi, respectively. In Equation 1, j's (from 1 to m) represent the intersected voxels that have to be found.
The quantitative PET reconstruction requires the system response matrix to be as accurate as possible. Thus, a basic requirement is to accurately find all voxels that can contribute to a given pair of crystals 10. In the clinic, the speed of reconstruction is also very important. Therefore, a fast and accurate algorithm is needed to meet this requirement.